调和分析及其应用中的一些问题
本书特色
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陆善镇教授专攻调和分析及其应用，特别是在bochner-riesz平均、奇异积分和振荡积分算子有界性以及函数空间理论方面做出了重要的贡献。他培养了一大批优秀的中青年数学工作者并成为中国调和分析及其应用领域的中坚力量。陆先生曾担任北京师范大学校长，现担任温州-肯恩大学校长。李俊峰、李晓春、陆国震编写的《调和分析及其应用中的一些问题(英文版)(精)》内容定位于陆善镇教授做出重要成就及感兴趣的领域，汇集了多位国际著名数学家以及陆先生的朋友和学生撰写的学术论文，包括了calderón-zygmund奇异积分算子理论以及局部tb定理、多线性奇异积分算子和fourier乘子理论、多线性嵌入定理、流形上特征函数的模估计、带权不等式、非线性schrodinger方程、函数空间理论等方面的一些问题的*新进展。本书将有益于调和分析及其相关领域的研究者以及硕士生、博士生。
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目录
multilinear embedding and hardy’s inequality william beckner 1 multilinear convolution inequalities 2 diagonal trace restriction for hardy’s inequality 3 diagonal trace restriction for a multilinear fractional integral 4 multilinear integrals and rearrangement acknowledgements referencesreal-variable theory of orlicz-type function spaces associated with operators — a survey der-chen chang, dachun yang and sibei yang 1 introduction 2 orlicz type spaces associated with operators satisfying poisson estimates 3 musielak-orlicz type spaces associated with nonnegative self-adjoint operators satisfying davies-gaffney estimates 4 musielak-orlicz type spaces associated with operators satisfying bounded ha-functional calculus acknowledgements referencesboundedness of rough strongly singular integral operators jiecheng chen, dashan fan and meng wang 1 lp –+ lq boundedness on rough operators 2 the phase function is not radial 3 the kernel satisfies a lipschitz condition 4 the kernel is ca referenceson the dimension dependence of some weighted inequalities alberto criado and fernando soria 1 introduction 2 the maximal operator over radial functions 3 proofs of the main results 4 kakeya maximal operator acknowledgements referenceslp estimates for multi-parameter and multilinear fourier multipliers and pseudo-differential operators wei dai, guozhen lu and lu zhang 1 introduction 2 lp estimates for multi-parameter and multi-linear paraproducts, multipliers and pseudo-differential operators 3 lp estimates for bilinear and multi-parameter hilbert transforms . . 4 lp estimates for bilinear operators given by non-smooth symbols with one-dimensional singularity set in the range 1/2 < p < 2/3 acknowledgements referencesexistence and uniqueness theory for the fractional schrsdinger equation on the torus seckin demirbas, m. burak erdoan and nikolaos tzirakis 1 introduction 2 notation and preliminaries 3 strichartz estimates 4 local well-posedness via the x8,b method 5 a smoothing estimate 6 global well-posedness via high-low frequency decomposition referencescompactness of maximal commutators of bilinear calder6n-zygmund singular integral operators yong ding, ting mei and qingying xue 1 tntrn(tnetinn nh rn r,it 2 the proof of theorem 1.1 3 the proof of theorem 1.2 referencesweak hardy spaces loukas grafakos and danqing he 1 introduction 2 relevant background 3 the proof of theorem 1 4 properties of hp' 5 square function characterization of hp' referencesa local tb theorem with vector-valued testing functions... ana grau de la herren and steve hofmann 1 introduction, history, preliminaries 2 a local tb theorem with vector-valued testing functions 3 application of theorem 2.13 to the theory of layer potentials . 4 appendix: a generalized christ-journ@ t1 theorem for square functions referencesnon-homogeneous local t1 theorem" dual exponents michael t. lacey and antti v. vdhdkangas 1 introduction 2 preliminaries 3 perturbations and a basic decomposition 4 a stopping tree construction 5 the inside-paraproduct term 6 the inside-stopping/error term 7 the separated term 8 preparations for the nearby term 9 the nearby-non-boundary term 10 the nearby-boundary term referencesthe dynamics of the nls with the combined terms in five and higher dimensions changxing miao, guixiang xu and lifeng zhao 1 introduction 2 preliminaries 3 variational characterization 4 part i: blow up for k:- . 5 profile decomposition 6 part ii: gwp and scattering for ]c+ acknowledgements referencessharp estimates for bilinear fourier multiplier operators akihiko miyachi and naohito tomita 1 introduction 2 product type sobolev scale 3 estimates for l2 x l --, l2 4 estimates for h1 x l -- l1 5 estimates for l x l --, bmo 6 estimates for h1 x h1 l1/2 7 estimates for h1 x l l2/3 8 proof of the only if part 9 isotropic besov scale referencesweighted estimates for fractional type marcinkiewicz integral operators associated to surfaces yoshihiro sawano and ksz6 yabuta 1 introduction 2 preparation for the proof of theorem 3 3 proof of theorem 3 4 proof of proposition 1 5 appendix: complex interpolation of homogeneous weighted triebel-lizorkin spaces references commutator estimates for the dirichlet-to-neumann map in lipschitz domains zhongwei shen 1 introduction 2 dahlberg's bilinear estimate, part i 3 dahlberg's bilinear estimate, part ii 4 trilinear estimates and proof of theorem 1.1 5 proof of theorem 1.2 referencesa note on lp-norms of quasi-modes christopher d. sogge and steve zelditch 1 introduction and main results 2 proof that proposition 1.3 implies theorems 1.1 and 1.2 3 proof of proposition 1.3 4 applications to breaking convexity bounds referencesastalas conjecture from the point of view of singular integrals on metric spaces alexander volberg 1 introduction 2 a simple proof of theorem 1. the weighted estimate of ahlfors-beurling transform = unweighted estimate of a certain non-symmetric calder6n-zygmund operator on a metric space . . . 3 t1 theorem for non-homogeneous metric measure spaces acknowledgements references c.s.i. for besov spaces p'q(]) with (a, (p,q)) e (0, 1)x ((0, 1]x (0,1] {(1,1)}) jie xiao and zhiehun zhai 1 introduction 2 c.s.i 3 applications acknowledgements referencesa list of ph.d. students post-doctors and visiting scholars supervised by professor shanzhen lu and foreign collaborators who worked with professor shanzhen lu
封面
书名:调和分析及其应用中的一些问题
作者:李俊峰
页数:422
定价:¥98.0
出版社:高等教育出版社
出版日期:2015-08-01
ISBN:9787040430189
PDF电子书大小:58MB 高清扫描完整版